#include <Triangle.h>

Collaboration diagram for mirtk::Triangle:

Static Public Member Functions
static void	Angles (const double a[3], const double b[3], const double c[3], double angle[3])

static double	Area (const double a[3], const double b[3], const double c[3])

static double	Area2D (const double a[2], const double b[2], const double c[2])

static Vector3	AreaGradient (const double a[3], const double b[3], const double c[3])

static double	BoundingSphereRadius (const double a[3], const double b[3], const double c[3], double *center=nullptr)

static void	Center (const double a[3], const double b[3], const double c[3], double center[3])

static double	Cotangent (double a[3], double b[3], double c[3])

static double	DistanceBetweenCenters (const double a1[3], const double b1[3], const double c1[3], const double a2[3], const double b2[3], const double c2[3], double p1, double p2)
	Compute distance between triangle center points. More...

static double	DistanceBetweenCorners (const double a1[3], const double b1[3], const double c1[3], const double a2[3], const double b2[3], const double c2[3], double p1, double p2)
	Compute distance between closest corner points of two triangles. More...

static double	DistanceBetweenTriangles (const double a1[3], const double b1[3], const double c1[3], const double n1[3], const double a2[3], const double b2[3], const double c2[3], const double n2[3], double p1, double p2)
	Compute distance between closest points of two triangles.

static double	DistanceBetweenTriangles (const double a1[3], const double b1[3], const double c1[3], const double a2[3], const double b2[3], const double c2[3], double p1, double p2)
	Compute distance between closest points of two triangles. More...

static double	DoubleArea (const double a[3], const double b[3], const double c[3])

static double	DoubleArea2D (const double a[2], const double b[2], const double c[2])

static Vector3	DoubleAreaGradient (const double a[3], const double b[3], const double c[3])

static double	DoubleSignedArea2D (const double a[2], const double b[2], const double c[2])

static double	MaxAngle (const double a[3], const double b[3], const double c[3])

static double	MinAngle (const double a[3], const double b[3], const double c[3])

static void	Normal (const double a[3], const double b[3], const double c[3], double n[3])

static void	NormalDirection (const double a[3], const double b[3], const double c[3], double n[3])

static Matrix3x3	NormalDirectionJacobian (const double a[3], const double b[3], const double c[3])

static Matrix3x3	NormalJacobian (const double a[3], const double b[3], const double c[3])

static Matrix3x3	NormalJacobian (const double a[3], const double b[3], const double c[3], const Matrix3x3 &dn)

static Matrix3x3	NormalJacobian (const double n[3], const Matrix3x3 &dn)

static Matrix3x3	NormalJacobian (const Vector3 &n, const Matrix3x3 &dn)

static double	SignedArea2D (const double a[2], const double b[2], const double c[2])

static bool	TriangleTriangleIntersection (const double a1[3], const double b1[3], const double c1[3], const double a2[3], const double b2[3], const double c2[3])
	Tests whether two triangles intersect each other.

static bool	TriangleTriangleIntersection (const double a1[3], const double b1[3], const double c1[3], const double a2[3], const double b2[3], const double c2[3], int &coplanar, double p1, double p2)
	Tests whether two triangles intersect each other.

Detailed Description

Auxiliary class/static helper functions for triangulated surface meshes

Definition at line 35 of file Triangle.h.

Member Function Documentation

§ Angles()

void mirtk::Triangle::Angles	(	const double	a[3],
		const double	b[3],
		const double	c[3],
		double	angle[3]
	)

inlinestatic

Compute angle at triangle corners

Parameters

[in]	a	Position of triangle vertex A.
[in]	b	Position of triangle vertex B.
[in]	c	Position of triangle vertex C.
[out]	angle	Angles at triangle vertices in radians.

Definition at line 346 of file Triangle.h.

§ Area()

double mirtk::Triangle::Area	(	const double	a[3],
		const double	b[3],
		const double	c[3]
	)

inlinestatic

Compute area of triangle

Parameters

[in]	a	Position of triangle vertex A.
[in]	b	Position of triangle vertex B.
[in]	c	Position of triangle vertex C.

Returns: Area of triangle.

Definition at line 312 of file Triangle.h.

§ Area2D()

double mirtk::Triangle::Area2D	(	const double	a[2],
		const double	b[2],
		const double	c[2]
	)

inlinestatic

Compute area of triangle in 2D

Parameters

[in]	a	Position of triangle vertex A.
[in]	b	Position of triangle vertex B.
[in]	c	Position of triangle vertex C.

Returns: Area of triangle.

Definition at line 336 of file Triangle.h.

§ AreaGradient()

Vector3 mirtk::Triangle::AreaGradient	(	const double	a[3],
		const double	b[3],
		const double	c[3]
	)

inlinestatic

Partial derivative of triangle area w.r.t. coordinates of vertex A

Parameters

[in]	a	Position of triangle vertex A.
[in]	b	Position of triangle vertex B.
[in]	c	Position of triangle vertex C.

Returns: Partial derivatives of triangle area w.r.t. coordinates of vertex A.

Definition at line 483 of file Triangle.h.

§ BoundingSphereRadius()

double mirtk::Triangle::BoundingSphereRadius	(	const double	a[3],
		const double	b[3],
		const double	c[3],
		double *	center = `nullptr`
	)

inlinestatic

Compute center point of triangle

Parameters

[in]	a	Position of triangle vertex A.
[in]	b	Position of triangle vertex B.
[in]	c	Position of triangle vertex C.
[out]	center	Position of triangle center.

Returns: Radius of bounding sphere with optionally returned center point.

Definition at line 266 of file Triangle.h.

§ Center()

void mirtk::Triangle::Center	(	const double	a[3],
		const double	b[3],
		const double	c[3],
		double	center[3]
	)

inlinestatic

Compute center point of triangle

Parameters

[in]	a	Position of triangle vertex A.
[in]	b	Position of triangle vertex B.
[in]	c	Position of triangle vertex C.
[out]	center	Position of triangle center.

Definition at line 258 of file Triangle.h.

§ Cotangent()

double mirtk::Triangle::Cotangent	(	double	a[3],
		double	b[3],
		double	c[3]
	)

inlinestatic

Compute cotangent of angle ABC

Parameters

[in]	a	Position of triangle vertex A.
[in]	b	Position of triangle vertex B.
[in]	c	Position of triangle vertex C.

Returns: Cotangent of angle ABC (equals cotangent of angle CBA).

Definition at line 374 of file Triangle.h.

§ DistanceBetweenCenters()

double mirtk::Triangle::DistanceBetweenCenters	(	const double	a1[3],
		const double	b1[3],
		const double	c1[3],
		const double	a2[3],
		const double	b2[3],
		const double	c2[3],
		double *	p1,
		double *	p2
	)

inlinestatic

Compute distance between triangle center points.

Compute distance between two triangles.

Definition at line 495 of file Triangle.h.

§ DistanceBetweenCorners()

double mirtk::Triangle::DistanceBetweenCorners	(	const double	a1[3],
		const double	b1[3],
		const double	c1[3],
		const double	a2[3],
		const double	b2[3],
		const double	c2[3],
		double *	p1,
		double *	p2
	)

inlinestatic

Compute distance between closest corner points of two triangles.

Compute distance between two triangles.

Definition at line 507 of file Triangle.h.

§ DistanceBetweenTriangles()

double mirtk::Triangle::DistanceBetweenTriangles	(	const double	a1[3],
		const double	b1[3],
		const double	c1[3],
		const double	a2[3],
		const double	b2[3],
		const double	c2[3],
		double *	p1,
		double *	p2
	)

inlinestatic

Compute distance between closest points of two triangles.

Compute distance between two triangles.

Definition at line 546 of file Triangle.h.

§ DoubleArea()

double mirtk::Triangle::DoubleArea	(	const double	a[3],
		const double	b[3],
		const double	c[3]
	)

inlinestatic

Compute twice the area of triangle

Parameters

[in]	a	Position of triangle vertex A.
[in]	b	Position of triangle vertex B.
[in]	c	Position of triangle vertex C.

Returns: Twice the area of the triangle.

Definition at line 304 of file Triangle.h.

§ DoubleArea2D()

double mirtk::Triangle::DoubleArea2D	(	const double	a[2],
		const double	b[2],
		const double	c[2]
	)

inlinestatic

Compute twice the area of triangle in 2D

Parameters

[in]	a	Position of triangle vertex A.
[in]	b	Position of triangle vertex B.
[in]	c	Position of triangle vertex C.

Returns: Twice the area of the triangle.

Definition at line 330 of file Triangle.h.

§ DoubleAreaGradient()

Vector3 mirtk::Triangle::DoubleAreaGradient	(	const double	a[3],
		const double	b[3],
		const double	c[3]
	)

inlinestatic

Partial derivatives of twice the triangle area w.r.t. coordinates of vertex A

Parameters

[in]	a	Position of triangle vertex A.
[in]	b	Position of triangle vertex B.
[in]	c	Position of triangle vertex C.

Returns: Partial derivatives of twice the triangle area w.r.t. coordinates of vertex A.

Definition at line 474 of file Triangle.h.

§ DoubleSignedArea2D()

double mirtk::Triangle::DoubleSignedArea2D	(	const double	a[2],
		const double	b[2],
		const double	c[2]
	)

inlinestatic

Compute twice the area of triangle in 2D

Parameters

[in]	a	Position of triangle vertex A.
[in]	b	Position of triangle vertex B.
[in]	c	Position of triangle vertex C.

Returns: Twice the signed area of the triangle.

Definition at line 318 of file Triangle.h.

§ MaxAngle()

double mirtk::Triangle::MaxAngle	(	const double	a[3],
		const double	b[3],
		const double	c[3]
	)

inlinestatic

Compute maximum angle at triangle corners

Returns: Maximum angle in radians.

Definition at line 365 of file Triangle.h.

§ MinAngle()

double mirtk::Triangle::MinAngle	(	const double	a[3],
		const double	b[3],
		const double	c[3]
	)

inlinestatic

Compute minimum angle at triangle vertices

Returns: Minimum angle in radians.

Definition at line 357 of file Triangle.h.

§ Normal()

void mirtk::Triangle::Normal	(	const double	a[3],
		const double	b[3],
		const double	c[3],
		double	n[3]
	)

inlinestatic

Compute normal of triangle

Parameters

[in]	a	Position of triangle vertex A.
[in]	b	Position of triangle vertex B.
[in]	c	Position of triangle vertex C.
[out]	n	Triangle normal vector.

Definition at line 290 of file Triangle.h.

§ NormalDirection()

void mirtk::Triangle::NormalDirection	(	const double	a[3],
		const double	b[3],
		const double	c[3],
		double	n[3]
	)

inlinestatic

Compute normal direction of triangle

Parameters

[in]	a	Position of triangle vertex A.
[in]	b	Position of triangle vertex B.
[in]	c	Position of triangle vertex C.
[out]	n	Non-normalized triangle normal vector. The length of the resulting vector equals twice the triangle area.

Definition at line 281 of file Triangle.h.

§ NormalDirectionJacobian()

Matrix3x3 mirtk::Triangle::NormalDirectionJacobian	(	const double	a[3],
		const double	b[3],
		const double	c[3]
	)

inlinestatic

Partial derivatives of normal direction w.r.t. position of vertex A

Parameters

[in]	a	Position of triangle vertex A.
[in]	b	Position of triangle vertex B.
[in]	c	Position of triangle vertex C.

Returns: Partial derivatives of normal direction components w.r.t. coordinates of vertex A.

Definition at line 389 of file Triangle.h.

§ NormalJacobian() [1/4]

Matrix3x3 mirtk::Triangle::NormalJacobian	(	const double	a[3],
		const double	b[3],
		const double	c[3]
	)

inlinestatic

Partial derivatives of normal w.r.t. coordinates of vertex A

Parameters

[in]	a	Position of triangle vertex A.
[in]	b	Position of triangle vertex B.
[in]	c	Position of triangle vertex C.

Returns: Partial derivatives of normal components w.r.t. coordinates of vertex A.

Definition at line 467 of file Triangle.h.

§ NormalJacobian() [2/4]

Matrix3x3 mirtk::Triangle::NormalJacobian	(	const double	a[3],
		const double	b[3],
		const double	c[3],
		const Matrix3x3 &	dn
	)

inlinestatic

Partial derivatives of normal w.r.t. coordinates of vertex A

Parameters

[in]	a	Position of triangle vertex A.
[in]	b	Position of triangle vertex B.
[in]	c	Position of triangle vertex C.
[in]	dn	Partial derivatives of normal direction vector.

Returns: Partial derivatives of normal components w.r.t. coordinates of vertex A.

Definition at line 458 of file Triangle.h.

§ NormalJacobian() [3/4]

Matrix3x3 mirtk::Triangle::NormalJacobian	(	const double	n[3],
		const Matrix3x3 &	dn
	)

inlinestatic

Partial derivatives of normal w.r.t. coordinates of vertex A

Parameters

[in]	n	Triangle normal vector, i.e., normalized direction vector.
[in]	dn	Partial derivatives of normal direction vector.

Returns: Partial derivatives of normal components w.r.t. coordinates of vertex A.

Definition at line 435 of file Triangle.h.

§ NormalJacobian() [4/4]

Matrix3x3 mirtk::Triangle::NormalJacobian	(	const Vector3 &	n,
		const Matrix3x3 &	dn
	)

inlinestatic

Partial derivatives of normal w.r.t. coordinates of vertex A

Parameters

[in]	n	Triangle normal vector, i.e., normalized direction vector.
[in]	dn	Partial derivatives of normal direction vector.

Returns: Partial derivatives of normal components w.r.t. coordinates of vertex A.

Definition at line 412 of file Triangle.h.

§ SignedArea2D()

double mirtk::Triangle::SignedArea2D	(	const double	a[2],
		const double	b[2],
		const double	c[2]
	)

inlinestatic

Compute area of triangle in 2D

Parameters

[in]	a	Position of triangle vertex A.
[in]	b	Position of triangle vertex B.
[in]	c	Position of triangle vertex C.

Returns: Signed area of triangle.

Definition at line 324 of file Triangle.h.

The documentation for this class was generated from the following file:

Triangle.h

Static Public Member Functions

Detailed Description

Member Function Documentation

§ Angles()

§ Area()

§ Area2D()

§ AreaGradient()

§ BoundingSphereRadius()

§ Center()

§ Cotangent()

§ DistanceBetweenCenters()

§ DistanceBetweenCorners()

§ DistanceBetweenTriangles()

§ DoubleArea()

§ DoubleArea2D()

§ DoubleAreaGradient()

§ DoubleSignedArea2D()

§ MaxAngle()

§ MinAngle()

§ Normal()

§ NormalDirection()

§ NormalDirectionJacobian()

§ NormalJacobian() [1/4]

§ NormalJacobian() [2/4]

§ NormalJacobian() [3/4]

§ NormalJacobian() [4/4]

§ SignedArea2D()